Optimal. Leaf size=10 \[ 2 E\left (\left .\sin ^{-1}\left (\sqrt{x}\right )\right |-1\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0259154, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ 2 E\left (\left .\sin ^{-1}\left (\sqrt{x}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + x]/(Sqrt[1 - x]*Sqrt[x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.99296, size = 10, normalized size = 1. \[ 2 E\left (\operatorname{asin}{\left (\sqrt{x} \right )}\middle | -1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(1/2)/(1-x)**(1/2)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.26948, size = 104, normalized size = 10.4 \[ \frac{2 \sqrt{\frac{x-1}{x+1}} \sqrt{\frac{x+1}{x-1}} \left (\sqrt{x-1} \sqrt{\frac{x+1}{x-1}} x+\frac{i \sqrt{2} x E\left (i \sinh ^{-1}\left (\frac{\sqrt{2}}{\sqrt{x-1}}\right )|\frac{1}{2}\right )}{\sqrt{\frac{x}{x-1}}}\right )}{\sqrt{-(x-1) x}} \]
Warning: Unable to verify antiderivative.
[In] Integrate[Sqrt[1 + x]/(Sqrt[1 - x]*Sqrt[x]),x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.016, size = 39, normalized size = 3.9 \[ 2\,{\frac{\sqrt{2}\sqrt{-x} \left ({\it EllipticF} \left ( \sqrt{1+x},1/2\,\sqrt{2} \right ) -{\it EllipticE} \left ( \sqrt{1+x},1/2\,\sqrt{2} \right ) \right ) }{\sqrt{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(1/2)/(1-x)^(1/2)/x^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x + 1}}{\sqrt{x} \sqrt{-x + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(sqrt(x)*sqrt(-x + 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{x + 1}}{\sqrt{x} \sqrt{-x + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(sqrt(x)*sqrt(-x + 1)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x + 1}}{\sqrt{x} \sqrt{- x + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)**(1/2)/(1-x)**(1/2)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x + 1}}{\sqrt{x} \sqrt{-x + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(sqrt(x)*sqrt(-x + 1)),x, algorithm="giac")
[Out]